The water-cooled lithium-lead (PbLi) breeding blanket is one of the candidate systems considered for the implementation in the European Demonstration Power Plant (DEMO) nuclear fusion reactor. This concept employs PbLi liquid metal as tritium breeder and neutron multiplier, water pressurized at 15.5 MPa as the coolant, and EUROFER as the structural material. The current design is based on the single module segment approach and follows the requirements of the DEMO-2015 baseline design. The module is constituted by a basic toroidal-radial cell that is recursively repeated along the poloidal direction where the liquid metal flows along a radial-poloidal path. The heat generated by the fusion reactions is extracted by means of separate cooling systems for the breeding zone and the first wall. A back supporting structure is dedicated to withstand loads of the module during normal and off-normal operations. Water and PbLi manifolds are integrated with primary heat transport and tritium extraction systems. The status of the conceptual design is presented, critically discussing its rationale and main features as supported by neutronic, thermal-hydraulic, magneto-hydrodynamic, and thermo-mechanic analyses. Recent results are outlined, pointing out open issues and development needs.